Introduction

The structure and nature of waves confront radio amateurs with fundamental questions at every step they take deeper into the physics of radio communication. This may sound trivial at first, but the subject can quickly become extraordinarily complex.

Matter, which surrounds us in all conceivable forms – here on Earth and throughout the universe – has two fundamental aspects to its behaviour. It can exhibit the properties of both particles and waves.

In 1687, Isaac Newton published his Principia Mathematica, establishing the foundations of classical mechanics. Macroscopic physical phenomena can generally be described without having to consider the behaviour of individual atoms. The mathematics underlying Newtonian mechanics is primarily based on algebra, calculus and differential equations. It describes a world in which physical quantities can, in principle, be assigned well-defined values at every point in time.

For example:

F = m · a

Force equals mass times acceleration.

Or:

x(t) = A · cos(ωt)

The equation of harmonic oscillation, describing the position of an object as a function of time, with amplitude A and angular frequency ω.

Quantum physics, on the other hand, began to emerge with the discovery and explanation of the double-slit experiment. In 1801–1803, Thomas Young demonstrated the wave nature of light, complementing the already established understanding of its particle-like properties.

Almost a century later, Max Planck made a groundbreaking discovery by introducing the concept of energy quanta. His work led to the fundamental physical constant now known as Planck's constant, h.

E = h · f

Energy is exchanged in discrete quantities, proportional to the frequency f, with Planck's constant having the value:

h = 6.626 × 10⁻³⁴ J·s

Subsequent developments made it clear that quantum theory is not limited to light or electromagnetic radiation. It must be applied to all known types of matter, including atoms and their constituent particles. The crucial point is that quantum effects become particularly significant when the physical quantities involved are comparable to the relevant quantum scales.

Below is the famous Schrödinger equation, published by Erwin Schrödinger in 1926. With this equation, he introduced a fundamentally new mathematical description of the quantum world.

The solutions to this differential equation reveal an entirely new perspective on physical reality. Instead of assigning particles definite positions and momenta at all times, quantum mechanics describes their possible states in terms of probability amplitudes. These allow us to calculate the probabilities of finding a particle at a particular location or measuring a specific energy.

The familiar picture of a world governed by precisely defined quantities, as in Newtonian mechanics, is no longer sufficient.

Since all matter surrounding us consists of atoms and particles, we are faced with two apparently very different descriptions of physical reality: classical mechanics and quantum physics.

Viewed on a macroscopic scale, the enormous number of particles making up matter behaves in a way that can be described remarkably well by Newton's classical laws. But when we look deeper into the microscopic world, matter reveals a very different set of properties, many of which challenge our everyday understanding of reality.

At this level, the role of fields and energy becomes increasingly important. Photons, for example, are the quantum particles of the electromagnetic field. They are also the carriers of electromagnetic energy and momentum.

And here we encounter one of the most fascinating aspects of modern physics: photons and electrons exhibit both particle-like and wave-like behaviour.